The chance of throwing at least $9$ in a single throw with two dice is:

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$ and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are

When a die is thrown twice,what is the probability of getting $4, 5,$ or $6$ on the first throw and $1, 2, 3,$ or $4$ on the second throw?

When two dice are thrown simultaneously,what is the probability that at least one of the dice shows a number greater than $3$?

When two dice are thrown,the probability of getting the sum of the values on them as $10$ or $11$ is

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is: